Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.

1 Right Triangle Trigonometry 2

1.1 Angles, Degrees, and Triangles 4

1.2 Similar Triangles 16

1.3 Definition 1 of Trigonometric Functions: Right Triangle Ratios 25

1.4 Evaluating Trigonometric Functions: Exactly and with Calculators 34

1.5 Solving Right Triangles 44

Review 57

Review Exercises 60

Practice Test 63

2 Trigonometric Functions 64

2.1 Angles in the Cartesian Plane 66

2.2 Definition 2 of Trigonometric Functions: The Cartesian Plane 73

2.3 Evaluating Trigonometric Functions for Nonacute Angles 81

2.4 Basic Trigonometric Identities 96

Review 106

Review Exercises 108

Practice Test 110

Cumulative Test 111

3 Radian Measure and the Unit Circle Approach 112

3.1 Radian Measure 114

3.2 Arc Length and Area of a Circular Sector 125

3.3 Linear and Angular Speeds 135

3.4 Definition 3 of Trigonometric Functions: Unit Circle Approach 143

Review 154

Review Exercises 156

Practice Test 158

Cumulative Test 159

4 Graphing Trigonometric Functions 160

4.1 Basic Graphs of Sine and Cosine Functions: Amplitude and Period 162

4.2 Translations of the Sine and Cosine Functions: Addition of Ordinates 184

4.3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 204

Review 222

Review Exercises 225

Practice Test 228

Cumulative Test 229

5 Trigonometric Identities 230

5.1 Trigonometric Identities 232

5.2 Sum and Difference Identities 242

5.3 Double-Angle Identities 255

5.4 Half-Angle Identities 264

5.5 Product-To-Sum and Sum-To-Product Identities 274

Review 283

Review Exercises 285

Practice Test 288

Cumulative Test 289

6 Solving Trigonometric Equations 290

6.1 Inverse Trigonometric Functions 292

6.2 Solving Trigonometric Equations That Involve Only One Trigonometric Function 314

6.3 Solving Trigonometric Equations That Involve Multiple Trigonometric Functions 325

Review 332

Review Exercises 335

Practice Test 336

Cumulative Test 337

7 Applications of Trigonometry: Triangles and Vectors 338

7.1 Oblique Triangles and the Law of Sines 340

7.2 The Law of Cosines 355

7.3 The Area of a Triangle 365

7.4 Vectors 373

7.5 The Dot Product 389

Review 397

Review Exercises 399

Practice Test 402

Cumulative Test 403

8 Complex Numbers, Polar Coordinates, and Parametric Equations 404

8.1 Complex Numbers 406

8.2 Polar (Trigonometric) Form of Complex Numbers 413

8.3 Products, Quotients, Powers, and Roots of Complex Numbers; De Moivre’s Theorem 422

8.4 Polar Equations and Graphs 435

8.5 Parametric Equations and Graphs 449

Review 458

Review Exercises 460

Practice Test 462

Cumulative Test 463

Appendix A Algebraic Prerequisites and Review 464

A.1 Factoring Polynomials 465

A.2 Basic Tools: Cartesian Plane, Distance, and Midpoint 477

A.3 Graphing Equations: Point-Plotting, Intercepts, and Symmetry 484

A.4 Functions 496

A.5 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 514

A.6 Graphing Techniques: Transformations 534

A.7 Operations on Functions and Composition of Functions 548

A.8 One-To-One Functions and Inverse Functions 558

Review 572

Review Exercises 575

Practice Test 579

Appendix B Conic Sections 581

B.1 Conic Basics 582

B.2 The Parabola 585

B.3 The Ellipse 598

B.4 The Hyperbola 610

B.5 Rotation of Axes 622

B.6 Polar Equations of Conics 632

Review 643

Review Exercises 646

Practice Test 649

Answers to Odd-Numbered Exercises 651

Applications Index 687

Subject Index 689

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